Advice from previous posters is generally pretty good. The application of lime is done to raise soil pH, as certain nutrients become unavailable to the plants below a certain level (usually between 6.0 and 7.0 is optimal, but variable by species). If you're in NC, chances are good that your soil will have a fair amount of clay in it, in which case pH is likely to be on the lower end, but a soil test from your state university's lab may be the most cost-effective way to determine your actual soil chemistry. If this is indeed the case, moderate application of lime probably won't hurt.
RE: the poorly-draining area - poor drainage can be caused by a variety of factors, but the two most common are 1.) subsurface obstructions/debris and 2.) compacted or unbalanced soil structure, or some combination of these two. Many site issues like poor drainage are the result of scars left on the landscape from the original building construction, often resulting in subsurface compaction which creates problems 1 and 2 above. In many cases, construction rubble with no horticultural value is lumped in with the fill, which creates really terrible subsoil conditions that don't really show up until you try to grow plants. Soil drainage can vary widely across even a small yard - I have personally observed projects where one area will barely absorb anything and 20' away you could stick a fire hose in the ground and have no surface water (I say 'projects' because I'm a landscape architect, so I see this fairly often). In some cases, tilling this area up and adding sand to the mix when backfilling can be helpful, but take care to contact whatever local authorities you need to before digging REALLY deep so as not to disturb any utilities that may be down there.
As others have suggested, the first step is to determine whether you indeed want this area to be turf. If so, I'd echo what others have said about choosing either a native grass or one that is adapted to your climate. Think about what activities you want to accommodate in your yard, whether you'd like a garden, how much maintenance you're realistically going to want to do (or have others do); thinking through how you will use it can help you maximize the utility you get out of your space.
Most state universities (and other large ones with reputable landscape architecture programs) will have searchable online databases that can tell you everything you'd ever want to know about what plants and turfgrasses are adapted for your area, what kind of soils they need, ornamental characteristics, etc. May be helpful if considering alternatives to lawn, and there are plenty of beautiful ones, indeed!
Have fun playing in the dirt!
